For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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5answers
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Jamie rolls a die multiple times. find the probability that she rolls her first 5 before she rolls her second even number

Jamie rolls her fair 6-sided die multiple times. Find the probability that she rolls her first 5 before she rolls her second (not necessarily distinct) even number? This is what I have so far... ...
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2answers
34 views

Expected value of a die when decision to role again depends on previous outcome

(Introduction to Probability, Blitzstein and Nwang) A fair die is rolled some number of times. You can choose whether to stop after 1, 2, or 3 rolls, and your decision can be based on the ...
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1answer
46 views

Getting a simultaneous first $6$ with two dice

What's the probability that two players that each throw a normal dice get their first six at the same time ? Let $X_k,Y_k$ denote the numbers obtained with the first ($X$) and second ($Y$) dice at ...
1
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1answer
46 views

Uniform distribution of the sum of two dice

Is it possible to build two dice such that the sum of the two dice follows an uniform distribution on $\{2,\dots,12\}$ ? EDIT : Both dice must have sides 1-6, but the probability that the dice falls ...
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0answers
45 views
3
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1answer
47 views

What's the probability of rolling 10 dice each with 10 sides and each will have to same number?

I think the probability is $1\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}={1\over 10^9}={1\over ...
2
votes
1answer
37 views

What is the probability of not rolling any given number on 10 rolls of a die?

In other words, ALL combinations which don't contain at least one of the number from 1-6 would count. So for example... 5, 2, 3, 3, 4, 1, 5, 5, 3, 1 would be counted because there is no 6 Also 5, ...
3
votes
3answers
70 views

Calculating the probability that throwing two dice will yield a higher number than throwing one die

How do I work out the probability that Andy, rolling two dice, will roll a number higher than Candy, rolling one die? The highest number you can roll with one die is six. The probability of rolling ...
2
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1answer
42 views

what is a formula for working out dice chance percentages?

I am not a student or a maths type person. Instead I play a lot of board games and one in particular. Arkham Horror / Eldritch Horror. It uses a dice system to calculate successful rolls and I would ...
7
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3answers
143 views

Roll a fair die until a 6 appears for the third time. What is the chance that all six values have occurred?

The question in the title is a homework question that I have been stumped on for some time. My approach thus far was to treat it as an occupancy problem. From class we derived the following formula ...
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2answers
65 views
-1
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1answer
73 views

Probability of rolling two dice

Consider two dice, each one having one face showing the letter a, two faces showing the letter b, and the remaining three faces showing the letter c. You roll each >die once, independently of the ...
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1answer
29 views

Probability that at least two $9$'s appear as sum in four tosses of a Pair of fair Dice.

I can calculate in the following way : $P(9 \text{ in one toss}) = 1/9$ sum the following : $P(9 \text{ in two toss})$, $P(9 \text{ in three toss})$, $P(9 \text{ in 4 toss})$ And the answer I get ...
0
votes
2answers
71 views

Trick dice Probability

I was given this exercise: We have 2 dice, the first is normal $\Omega = \left\{1,2,...,6 \right\}$ and the other is a trick dice, with sample space $\Omega = \left\{2,3,4,5,6,6 \right\}$. If there ...
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2answers
26 views

Probability of dice rolls

Two regular cubic dice are rolled. One is red and the other blue. What s the probability that the red die roll is greater that or equal to the blue die?
1
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1answer
31 views

Probability of getting n amount of each number from 1-6 after 6n rolls of a dice

I managed to figure this out for n = 1. $ \frac{6}{6} \times \frac{5}{6} \times \frac{4}{6} \times \frac{3}{6} \times \frac{2}{6} \times \frac{1}{6} $ I thought it would work by putting this to the ...
0
votes
2answers
22 views

Probability of selecting a biased coin?

Me and a few classmates were working through a probability & statistics past paper: We have two coins denoted H1 and H2. Coin H1 is fair, i.e. $P(h) = P(t)$ $= 1/2$, $h$ being head and $t$ ...
0
votes
2answers
71 views

A tough dice probability conundrum

There are 2 fair die. You randomly roll them at the same time. To win is to have the sum of the die or some combination of the sum or the value of each die cover the numbers 1-9 inclusive. You can ...
14
votes
3answers
2k views

Six throws, only two distinct numbers: coincidence?

My daughter threw a die (D6) six times and got: 6,2,2,6,2,6. This got us wondering whether having only two distinct numbers come up in six throws was very unlikely or would happen fairly often. How ...
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2answers
66 views

Probability in dice rolls

$A$ rolls a standard $6$ sided die $20$ times while $B$ rolls it $21$ times. Find the probability that $A$'s outcome is more than $B$'s. Here, outcome means the sum of the numbers appearing on all ...
2
votes
6answers
70 views

Expectation of two dice game

The game plays like this: You roll two dices at the same time. If you get same number on both dices, you have to roll again, until you get different numbers. If you get different numbers, you stop. ...
3
votes
1answer
25 views

Have face-transitive polyhedra been completely classified?

I've been researching polyhedral dice, and everywhere I look it states that face-transitive (and therefore fair) dice include polyhedra of various families, like the platonic solids, catalan solids, ...
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2answers
53 views

Dice: Probability of rolling a number between two other dice throws

I was pretty suprised about this problem when I encountered it in one of my excercise sheets and would like to ask for an approach here because I have no idea how I'm supposed to get started here: ...
0
votes
1answer
41 views

Binomial Probability (Dice)

The throwing of a one or two is called a success. The six dice are thrown together 64 times and the frequencies of the throws with 0, 1, 2,..., 6 successes are summed over all six pairs are as ...
22
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6answers
3k views

What are the odds of hitting exactly 100 rolling a fair die

I roll a fair die and sequentially sum the numbers the die shows. What are the odds the summation will hit exactly 100? More generally, what are the odds of hitting an exact target number t while ...
0
votes
1answer
63 views

Conditional Entropy in rolling a dice

A 6-sided die is tossed once. Two events X and Y are defined. X is the event in which an even number comes up and Y is the event in which the number is a multiple of 3. The value of H(X|Y) needs to be ...
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2answers
56 views

Independent dice throw

I need help on this question regarding dice and probability. The question is, that a dice throws three times independently of each other. The random variable $X$ denotes the number of sides on the ...
0
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3answers
109 views

What's the probability of rolling the same number twice with a pair of dice?

There are a number of questions similar to this, but I'm asking about rolling two dice twice, not one die two times. Or I guess you could think of it as 4 dice total, with each pair distinguishable. ...
1
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1answer
65 views

Throw X dice, sum face $1,2,3,4$ minus Y, then add $ 5,6$ formula

I am trying to program something to find out the probability of all sum possible when I throw $X$ dice, sum all the face showing $1,2,3,4$ then I minus $Y$ from that sum (with a minimum of $0$, no ...
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2answers
73 views

Reroll 2 dice sum probability

My statistics are very far in my memory and I am not a math guru so I do not understand half of fuzy symbols used in most post that could have the answer I am looking for. So I would ask for a very ...
0
votes
2answers
54 views

Chevalier de Méré's Problem Type Question

Is the following argument correct: A double six in a single turn in game B is 1/6 as likely as rolling a six in one turn in game A. But there are 6 times as many turns in game B as game A. Thus the ...
3
votes
3answers
459 views

Probably of 2 six in 5 dice rolls

What is the probability of obtaining exatcly 2 six when rolling a dice 5 times? In order to obtain this probability, I will need to devide the number of favorable events by the number of possible ...
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4answers
82 views

Rephrasing die question

Seems I asked my last questions poorly and it got a bad response. Okay so basically here's the problem and I will explain how I am trying to do it. You roll 1 fair die repeatedly until you either ...
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1answer
66 views

Probability Rolling a dice until you get 1/2 or 2/2 [closed]

You roll $1$ die repeatedly until you get a $1$ immediately followed by a $2$ or a $2$ immediately followed by a $2$. What is the probability that a $1$ then a $2$ is rolled before a $2$ then a $2$? ...
0
votes
1answer
53 views

Calculate the Entropy Change if 5 Previously Tossed Dice Are Turned to All “1”

Relevant Equations: S = Boltzmann*ln(W) where S is entropy and W is the number of microstates. I have thought about this two ways. 1 way. Look at each die separately. Let macrostate 1 = number of ...
0
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1answer
67 views

Three dice rolled

Three indistinguishable (fair) dice are thrown simultaneously at random. Find the probability that the sum of the three dice is less than six and that no two dice show the same face (the same number). ...
0
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1answer
32 views

Probability of Fair Die

Hi everyone I have a question about probability: Fair die thrown two times, final score is calculated as follows. If the number on the second throw is a 5 he multiplies the two numbers together, and ...
2
votes
1answer
61 views

The math behind generating Dungeons & Dragons ability scores: roll 4d6, toss lowest

D&D 5th ed. gives the following instructions for determining your “ability scores.” Roll four 6-sided dice and record the total of the highest three dice If I repeat the ...
0
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2answers
51 views

How to find the probability of a score from multiple dice with varying sides

I'm trying to find a general method for working out the probability of a score from rolling several dice with varying sides. For example, the probability of getting a result of 12 when rolling two ...
1
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1answer
26 views

Conditional Expectation of Two Dice Roll?

A is the first roll of the dice, B is the second. The question is to find the expected value of A given A + B = 7; E(A|A+B = 7) Since A can be any number between 1 and 6, is this as simple as ...
2
votes
4answers
54 views

Simple combinatorics dice problem

How would you explain, how ${5\choose4}$ corresponds to the pattern $6-6-6-6-3$ when throwing five dice. The pattern is meant to form a sum of $27$ in total. What I do understand is that you could ...
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4answers
93 views

Dice rolling probability. [closed]

A die (6 face) is thrown 3 times. What is the probability that the second and third rolls are larger then the first roll. Thank you
0
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0answers
85 views

A game of dice for you guys

You throw n number of dice of D sides for each dice (i.e.: D6, D10, etc...), all dice of the same D (you can suppose that the distribution of values over D is homogeneous, just multiplicity of 1 as in ...
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0answers
75 views

Two dice are rolled. If the sum is greater than 8, what is the probability that it is 11?

Two dice are rolled. If the sum is greater than 8, what is the probability that it is 11? I'm not sure if this question is asking for conditional probability or just 2/10...
3
votes
5answers
153 views

Expectation and best strategy for a dice game

I am somewhat stuck on this problem, it should be straightforward but I cannot find a clearly explained solution: A single dice is rolled as many times as you want. For each throw, you receive n ...
0
votes
3answers
39 views

Die Roll Probability with 8-sided Die

What is the probability of rolling an "8" on an 8-sided die four times out of nine attempts? My friends and I were playing a game where one player could only succeed by rolling an 8 with an eight ...
2
votes
3answers
77 views

probability rolling a dice 5 times

I can't solve this problem: What is the probability that, when rolling a dice 5 times, the number of times when you get a 1 or 2 is greater than the number of times when you get a 6. any help?
9
votes
2answers
680 views

What is the probability of my sum reaching exactly 10? [closed]

I throw a 6-sided dice (with values: 0,1,2,3,4,5) multiple times and add each value to a sum, which is 0 in the beginning. What is the probability of my sum reaching exactly 10, 11, 12, 13, 14? After ...
1
vote
1answer
108 views

Fudge Dice: Reroll vs. Bonus

A "fudge die" is a die with equal probability to result in -1, 0, or +1. The commercially produced fudge dice are generally 6-sided dice with two "–", two "+", and two blank sides. In the ...
3
votes
0answers
82 views

Dice: Expected highest value with a tricky condition

I know how to calculate the expected value "E" of a roll of n k-sided dice if we are supposed to keep the highest number rolled. If I am not wrong, the formula is: E = k − (1^n + 2^n + ... + ...